A student has to appear for exam in 7 subjects. Certain minimum marks are required to pass in the subject. He fails if he does not reach to the level of minimum marks required in at least one of 7 subjects.

Total combinations in which a student can fail

= ^{7}C_{1} + ^{7}C_{2} + ^{7}C_{3} + ^{7}C_{4} + ^{7}C_{5} + ^{7}C_{6} + ^{7}C_{7}

= 7 + \(\frac{7×6}{2×1}+\frac{7×6×5}{3×2×1}+\frac{7×6×5×4}{4×3×2×1}+\frac{7×6×5×4×3}{5×4×3×2×1}\) + 7 + 1

= 7 + 21 + 35 + 35 + 21 + 7 + 1

= 127